TY - JOUR A1 - Schwarzl, Maria A1 - Godec, Aljaz A1 - Oshanin, Gleb A1 - Metzler, Ralf T1 - A single predator charging a herd of prey: effects of self volume and predator-prey decision-making JF - Journal of physics : A, Mathematical and theoretical N2 - We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant. KW - first passage process KW - diffusion KW - predator-prey model Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/22/225601 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Sandev, T. A1 - Iomin, Alexander A1 - Kantz, Holger A1 - Metzler, Ralf A1 - Chechkin, Aleksei V. T1 - Comb Model with Slow and Ultraslow Diffusion JF - Mathematical modelling of natural phenomena N2 - We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process. KW - comb-like model KW - anomalous diffusion KW - mean squared displacement KW - probability density function Y1 - 2016 U6 - https://doi.org/10.1051/mmnp/201611302 SN - 0973-5348 SN - 1760-6101 VL - 11 SP - 18 EP - 33 PB - EDP Sciences CY - Les Ulis ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Chechkin, Aleksei V. A1 - Klages, Rainer A1 - Metzler, Ralf T1 - Search reliability and search efficiency of combined Levy-Brownian motion: long relocations mingled with thorough local exploration JF - Journal of physics : A, Mathematical and theoretical N2 - A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent alpha < 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent a of the Levy flight component. KW - random search process KW - first passage KW - first arrival KW - Levy flights KW - Brownian motion Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/39/394002 SN - 1751-8113 SN - 1751-8121 VL - 49 SP - 2189 EP - 2193 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Metzler, Ralf A1 - Jeon, J. -H. A1 - Cherstvy, Andrey G. T1 - Non-Brownian diffusion in lipid membranes: Experiments and simulations JF - Biochimica et biophysica acta : Biomembranes N2 - The dynamics of constituents and the surface response of cellular membranes also in connection to the binding of various particles and macromolecules to the membrane are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder through the addition of cholesterol or proteins and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Rog. (C) 2016 The Authors. Published by Elsevier B.V. KW - Lipid bilayer KW - Protein crowding KW - Anomalous diffusion KW - Simulations KW - Stochastic modelling KW - Non-Gaussian Y1 - 2016 U6 - https://doi.org/10.1016/j.bbamem.2016.01.022 SN - 0005-2736 SN - 0006-3002 VL - 1858 SP - 2451 EP - 2467 PB - Elsevier CY - Amsterdam ER - TY - GEN A1 - Metzler, Ralf T1 - PROTEIN PHYSICS Forever ageing T2 - Nature physics N2 - Single-molecule techniques have long given us insight into the motion and interactions of individual molecules. But simulations now show that the dynamics inside single proteins is not as simple as we thought — and that proteins are forever changing. Y1 - 2016 U6 - https://doi.org/10.1038/nphys3585 SN - 1745-2473 SN - 1745-2481 VL - 12 SP - 113 EP - 114 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Kruesemann, Henning A1 - Schwarzl, Richard A1 - Metzler, Ralf T1 - Ageing Scher-Montroll Transport JF - Transport in Porous Media N2 - We study the properties of ageing Scher-Montroll transport in terms of a biased subdiffusive continuous time random walk in which the waiting times between consecutive jumps of the charge carriers are distributed according to the power law probability with . As we show, the dynamical properties of the Scher-Montroll transport depend on the ageing time span between the initial preparation of the system and the start of the observation. The Scher-Montroll transport theory was originally shown to describe the photocurrent in amorphous solids in the presence of an external electric field, but it has since been used in many other fields of physical sciences, in particular also in the geophysical context for the description of the transport of tracer particles in subsurface aquifers. In the absence of ageing () the photocurrent of the classical Scher-Montroll model or the breakthrough curves in the groundwater context exhibit a crossover between two power law regimes in time with the scaling exponents and . In the presence of ageing a new power law regime and an initial plateau regime of the current emerge. We derive the different power law regimes and crossover times of the ageing Scher-Montroll transport and show excellent agreement with simulations of the process. Experimental data of ageing Scher-Montroll transport in polymeric semiconductors are shown to agree well with the predictions of our theory. KW - Anomalous diffusion KW - Ageing KW - Scher-Montroll transport Y1 - 2016 U6 - https://doi.org/10.1007/s11242-016-0686-y SN - 0169-3913 SN - 1573-1634 VL - 115 SP - 327 EP - 344 PB - Springer CY - New York ER - TY - JOUR A1 - Jeon, Jae-Hyung A1 - Javanainen, Matti A1 - Martinez-Seara, Hector A1 - Metzler, Ralf A1 - Vattulainen, Ilpo T1 - Protein Crowding in Lipid Bilayers Gives Rise to Non-Gaussian Anomalous Lateral Diffusion of Phospholipids and Proteins JF - Physical review : X, Expanding access N2 - Biomembranes are exceptionally crowded with proteins with typical protein-to-lipid ratios being around 1:50 - 1:100. Protein crowding has a decisive role in lateral membrane dynamics as shown by recent experimental and computational studies that have reported anomalous lateral diffusion of phospholipids and membrane proteins in crowded lipid membranes. Based on extensive simulations and stochastic modeling of the simulated trajectories, we here investigate in detail how increasing crowding by membrane proteins reshapes the stochastic characteristics of the anomalous lateral diffusion in lipid membranes. We observe that correlated Gaussian processes of the fractional Langevin equation type, identified as the stochastic mechanism behind lipid motion in noncrowded bilayer, no longer adequately describe the lipid and protein motion in crowded but otherwise identical membranes. It turns out that protein crowding gives rise to a multifractal, non-Gaussian, and spatiotemporally heterogeneous anomalous lateral diffusion on time scales from nanoseconds to, at least, tens of microseconds. Our investigation strongly suggests that the macromolecular complexity and spatiotemporal membrane heterogeneity in cellular membranes play critical roles in determining the stochastic nature of the lateral diffusion and, consequently, the associated dynamic phenomena within membranes. Clarifying the exact stochastic mechanism for various kinds of biological membranes is an important step towards a quantitative understanding of numerous intramembrane dynamic phenomena. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevX.6.021006 SN - 2160-3308 VL - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Godec, Aljaz A1 - Metzler, Ralf T1 - First passage time distribution in heterogeneity controlled kinetics: going beyond the mean first passage time JF - Scientific reports N2 - The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening series of new results focusing mostly on the so-called mean and global first passage time (MFPT and GFPT, respectively) of such processes. Here we push the understanding of first passage processes one step further. For a simple heterogeneous system we derive rigorously the complete distribution of first passage times (FPTs). Our results demonstrate that the typical FPT significantly differs from the MFPT, which corresponds to the long time behaviour of the FPT distribution. Conversely, the short time behaviour is shown to correspond to trajectories connecting directly from the initial value to the target. Remarkably, we reveal a previously overlooked third characteristic time scale of the first passage dynamics mirroring brief excursion away from the target. Y1 - 2016 U6 - https://doi.org/10.1038/srep20349 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Godec, Aljaz A1 - Metzler, Ralf T1 - Universal Proximity Effect in Target Search Kinetics in the Few-Encounter Limit JF - Physical review : X, Expanding access N2 - When does a diffusing particle reach its target for the first time? This first-passage time (FPT) problem is central to the kinetics of molecular reactions in chemistry and molecular biology. Here, we explain the behavior of smooth FPT densities, for which all moments are finite, and demonstrate universal yet generally non-Poissonian long-time asymptotics for a broad variety of transport processes. While Poisson-like asymptotics arise generically in the presence of an effective repulsion in the immediate vicinity of the target, a time-scale separation between direct and reflected indirect trajectories gives rise to a universal proximity effect: Direct paths, heading more or less straight from the point of release to the target, become typical and focused, with a narrow spread of the corresponding first-passage times. Conversely, statistically dominant indirect paths exploring the entire system tend to be massively dissimilar. The initial distance to the target particularly impacts gene regulatory or competitive stochastic processes, for which few binding events often determine the regulatory outcome. The proximity effect is independent of details of the transport, highlighting the robust character of the FPT features uncovered here. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevX.6.041037 SN - 2160-3308 VL - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Godec, Aljaz A1 - Metzler, Ralf T1 - Active transport improves the precision of linear long distance molecular signalling JF - Journal of physics : A, Mathematical and theoretical N2 - Molecular signalling in living cells occurs at low copy numbers and is thereby inherently limited by the noise imposed by thermal diffusion. The precision at which biochemical receptors can count signalling molecules is intimately related to the noise correlation time. In addition to passive thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can transiently bind to molecular motors and are actively transported across biological cells. Active transport is most beneficial when trafficking occurs over large distances, for instance up to the order of 1 metre in neurons. Here we explain how intermittent active transport allows for faster equilibration upon a change in concentration triggered by biochemical stimuli. Moreover, we show how intermittent active excursions induce qualitative changes in the noise in effectively one-dimensional systems such as dendrites. Thereby they allow for significantly improved signalling precision in the sense of a smaller relative deviation in the concentration read-out by the receptor. On the basis of linear response theory we derive the exact mean field precision limit for counting actively transported molecules. We explain how intermittent active excursions disrupt the recurrence in the molecular motion, thereby facilitating improved signalling accuracy. Our results provide a deeper understanding of how recurrence affects molecular signalling precision in biological cells and novel medical-diagnostic devices. KW - noise in biochemical signalling KW - Brownian motion KW - active transport KW - linear response theory KW - fluctuation-dissipation theorem KW - generalised Langevin equation KW - recurrence Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/36/364001 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets JF - Soft matter N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. Y1 - 2016 U6 - https://doi.org/10.1039/C6SM01522K SN - 1744-6848 SN - 1744-683X PB - RSC CY - London ER - TY - GEN A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 256 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95882 ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Petrov, Eugene P. A1 - Metzler, Ralf T1 - Interactions of rod-like particles on responsive elastic sheets JF - Soft matter N2 - What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed. Y1 - 2016 U6 - https://doi.org/10.1039/c6sm01522k SN - 1744-683X SN - 1744-6848 VL - 12 SP - 7908 EP - 7919 PB - Royal Society of Chemistry CY - Cambridge ER - TY - JOUR A1 - Ghosh, Surya K. A1 - Cherstvy, Andrey G. A1 - Grebenkov, Denis S. A1 - Metzler, Ralf T1 - Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments JF - NEW JOURNAL OF PHYSICS N2 - A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells. KW - anomalous diffusion KW - crowded fluids KW - stochastic processes Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/1/013027 SN - 1367-2630 VL - 18 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces BT - the nonlinear Poisson–Boltzmann approach JF - New journal of physics : the open-access journal for physics N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems. KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/8/083037 SN - 1367-2630 VL - 18 PB - IOP Publ. CY - London ER - TY - GEN A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces BT - the nonlinear Poisson–Boltzmann approach N2 - We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 292 KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-100295 ER - TY - JOUR A1 - de Carvalho, Sidney J. A1 - Metzler, Ralf A1 - Cherstvy, Andrey G. T1 - Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces: the nonlinear Poisson-Boltzmann approach JF - NEW JOURNAL OF PHYSICS N2 - We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces-are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye-Huckel approximation is often not feasible and the nonlinear Poisson-Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson-Boltzmann equation is smaller than the Debye-Huckel result, such that the required critical surface charge density for polyelectrolyte adsorption sigma(c) increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical-chemical and biophysical systems. KW - polyelectrolyte adsorption KW - electrostatic interactions KW - critical phenomena KW - Debye screening Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/8/083037 SN - 1367-2630 VL - 18 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes JF - Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion. Y1 - 2016 U6 - https://doi.org/10.1039/C6CP03101C SN - 1463-9084 SN - 1463-9076 VL - 18 SP - 23840 EP - 23852 PB - RSC Publ. CY - Cambridge ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 257 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-95901 SP - 23840 EP - 23852 ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Metzler, Ralf T1 - Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes JF - Physical chemistry, chemical physics : a journal of European Chemical Societies N2 - We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion. Y1 - 2016 U6 - https://doi.org/10.1039/c6cp03101c SN - 1463-9076 SN - 1463-9084 VL - 18 SP - 23840 EP - 23852 PB - Royal Society of Chemistry CY - Cambridge ER - TY - GEN A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion BT - (non-)existence of the overdamped limit in anomalous diffusion N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 267 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-97158 ER - TY - JOUR A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion BT - (non-)existence of the overdamped limit in anomalous diffusion JF - Scientific reports N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. Y1 - 2016 U6 - https://doi.org/10.1038/srep30520 SN - 2045-2322 VL - 6 PB - Nature Publishing Group CY - London ER - TY - JOUR A1 - Bodrova, Anna S. A1 - Chechkin, Aleksei V. A1 - Cherstvy, Andrey G. A1 - Safdari, Hadiseh A1 - Sokolov, Igor M. A1 - Metzler, Ralf T1 - Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion JF - Scientific reports N2 - It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases. Y1 - 2016 U6 - https://doi.org/10.1038/srep30520 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER -